Boundary Value-Free Magnetic Resonance Electrical Properties Tomography Based on the Generalized Cauchy Formula with the Complex-derivative Boundary Condition
Boundary Value-Free Magnetic Resonance Electrical Properties Tomography Based on the Generalized Cauchy Formula with the Complex-derivative Boundary Condition
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DOI：
10.2528/pierm20062202
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发表时间：
2020-01-01
影响因子：
1
通讯作者：
Nara, Takaaki
中科院分区：
文献类型：
--
作者：
Fushimi, Motofumi;Nara, Takaaki
最近，基于磁共振的电特性层析成像，其中的电特性（EP），即电导率和介电常数，生物组织的重建，一直是一个活跃的研究领域。我们以前提出了一个显式重建方法的基础上的Dbar方程和广义柯西公式给出的显式解。在这种方法中，在其他一些传统的方法，在感兴趣的区域的边界上的EP值必须指定的偏微分方程的Dirichlet边界条件。然而，在实际情况中很难知道精确的值。在本文中，我们提出了一种新的方法，重建EP没有边界EP值的先验信息，通过推导一个新的表示公式的Dbar方程的复导数边界条件的解决方案。数值模拟和体模实验表明，该方法可以重建EP的边界EP值不知道。因此，所提出的方法大大提高了目前的EPT方法的适用性，以实际情况。
Recently, magnetic-resonance-based electrical properties tomography, by which the electrical properties (EPs), namely conductivity and permittivity, of biological tissues are reconstructed, has been an active area of study. We previously proposed an explicit reconstruction method based on the Dbar equation and its explicit solution given by the generalized Cauchy formula. In this method, as in some other conventional methods, the values of EPs on the boundary of the region of interest must be specified by the Dirichlet boundary condition of the partial differential equation. However, it is difficult to know the precise values in practical situations. In this paper, we propose a novel method that reconstructs EPs without the prior information of boundary EP values by deriving a new representation formula of the solution of the Dbar equation with the complex-derivative boundary condition. Numerical simulations and phantom experiments show that the proposed method can reconstruct EPs without knowledge of the boundary EP values. Therefore, the proposed method greatly enhances the applicability of the current EPT methods to practical situations.